- 1 -

Sheet 1 (Revision) Prob # 1

A square tie bar 30 mm x 30 mm in section carries a load. It is attached to a

bracket by means of 8 bolts. Calculate the diameter of the bolt if the maximum

stress in the tie bar is 175 MPa and in the bolts is 85 MPa.

Prob # 2

Determine the maximum normal stress in the steel I section shown in the

figure. The flanges are 6 mm and the web is 3 mm thick.

N

Prob # 3

This problem illustrates that the factor of safety for a machine element

depends on the particular point selected for analysis. Here you are to compute

factors of safety, based upon the distortion-energy theory, for stress elements at

A and B of the member shown in the figure. The yield strength of this bar is 280

MPa and is loaded by the forces F = 0.55 kN, P = 8.0 kN, and T = 30 N.m.

N

250mm 125mm 125mm 7kN 7kN

40mm

70mm

Alexandria University

Faculty of Engineering

Electromechanically Department

Advanced Materials

8th term

2013

- 2 -

The figure shows a crank loaded by a force F = 800 N which causes twisting

and bending of the 20 mm diameter shaft fixed to a support at the origin of the

reference system. In actuality, the support may be an inertia which we wish to

rotate, but for the purposes of a strength analysis we can consider this to be a

statics problem. The yield strength of the shaft AB is 220 MPa. Using the

maximum-shear-stress theory, find the factor of safety based on the stress at

point A.

Prob # 4

- 3 -

Prob # 5

Solve Prob. 4 using the distortion energy theory. If you have solved Prob. 3,

compare the results and discuss the difference.

Prob # 6

The figure shows a shaft mounted in bearings at A and D and having pulleys

at B and C. The forces shown acting on the pulley surfaces represent the belt

tensions. The shaft is to be made of cast iron with the ultimate strength 210 MPa

using a factor of safety 2.8. What diameter should be used for the shaft?

Prob # 7

The figure is a schematic drawing of a countershaft that supports two belt

pulleys. For each pulley, the belt tensions are parallel. For pulley A consider the

loose belt tension is 15 percent of the tension on the tight side. The yield

strength of the shaft is 370 MPa. For a static analysis with a factor of safety of

3.0, determine the minimum preferred size diameter. Use the distortion-energy

theory.

- 4 -

Prob # 8

Find the thickness of a cast iron cylinder 250mm in diameter to carry a

pressure of 0.7 MPa. Take maximum tensile stress for cast iron as 14MPa.

Prob # 9

A spherical shell of 800 mm diameter is subjected to an internal pressure of 2

MPa. Find the thickness required for the shell if the safe stress is not to exceed

100 MPa.

Prob # 10

The pressure within cylinder of hydraulic press is 8.4 MPa. The inside

diameter of the cylinder is 25.4mm. Determine the thickness of the cylinder

wall, if the allowable tensile stress is 17.5 MPa.

- 5 -

Prob # 11

Develop specific Euler equations for the sizes of columns having

(a) Round cross sections

(b) Rectangular cross sections

Prob # 12

Specify the diameter of a round column 1.5 m long that is to carry a

maximum load estimated to be 22 kN. Use a design factor nd = 4 and consider

the ends as pinned (rounded). The column material selected has aminimum yield

strength of 500 MPa and a modulus of elasticity of 207 GPa.

The figure shows a schematic

drawing of a vehicular jack that is to

be designed to support a maximum

mass of 400 kg based on the use of a

design factor nd = 2.50. The

opposite-handed threads on the two

ends of the screw are cut to allow

the link angle θ to vary from 30◦ .

The links are to be machined from

AISI 1020 hot-rolled steel bars with a minimum yield strength of 380 MPa.

Each of the four links is to consist of two bars, one on each side of the central

bearings. The bars are to be 300 mm long and have a bar width of 25 mm. The

pinned ends are to be designed to secure an end-condition constant of at least C

= 1.4 for out-of-plane buckling. Find a suitable preferred thickness and the

resulting factor of safety for this thickness.

Prob # 13